REPRESENTATION OF THE BOUNDARY ELLIPTIC QUANTUM GROUP BE-TAU,ETA (SL(2)) AND THE BETHE-ANSATZ

We extend the Gervais-Neveu-Felder equation (GNFE) to the boundary cas e. Using the boundary GNFE, we give a definition of the boundary ellip tic quantum group BEtau,eta(sl(2)). The evaluation representation of t he boundary elliptic quantum group BEtau,eta(sl(2)) is presented. The Bethe ansatz for the boundary quantum group BEtau,eta(sl(2)) is obtain ed. In a special case, the obtained Bethe ansatz is similar to the Bet he ansatz of the eight-vertex and the higher spin eight-vertex models with open boundary conditions. (C) 1997 Elsevier Science B.V.